{
  "id": 340,
  "curve_key": "214985466336019117309074782217:-99194513381049262818490270326635852925998181",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-4478863882000398277272391296",
    "114808464561400729459593498162805258984396"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 202.6211038147347,
  "faltings_height": 14.719966568615408,
  "conductor": "41455086380717191185808070125299852614948356707622719536837037239971384494",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "67",
    "907",
    "492189681146015024152899098930855972467406576319834595366987250491"
  ],
  "discriminant": "56023261274818083684317895593068832776592402076388197065657911137049675053251242884",
  "regulator": "107950823401904672275211.002789114996797764365608600685292758274805529213099082",
  "points": [
    [
      "3959568700584289293/117649",
      "-1888919593160911716243688163/40353607"
    ],
    [
      "5983705942679832815/229441",
      "13788091865318344243182730294/109902239"
    ],
    [
      "2881285059776627",
      "154619119609581457020302"
    ],
    [
      "22604263646403854/625",
      "178019179057919383520258/15625"
    ],
    [
      "2501120224508696966/13225",
      "3735278267807866710637937216/1520875"
    ],
    [
      "493011317715364/9",
      "4966708714634479141658/27"
    ],
    [
      "2535873207907338494/12769",
      "3833338061428204981266167200/1442897"
    ],
    [
      "2621178175745556434/124609",
      "-7606344775984294549796004152/43986977"
    ],
    [
      "-1775646997704119939/90000",
      "11937974612173216911789469159/27000000"
    ],
    [
      "47472459163994606/961",
      "-3537936341989803306725536/29791"
    ],
    [
      "1567034501871269/49",
      "-22441168132146613189600/343"
    ],
    [
      "55057542053675",
      "-187379238442397134714"
    ],
    [
      "3723652938785579822/63001",
      "-3760784743567895785576713248/15813251"
    ],
    [
      "36382667185742",
      "3889906867339569056"
    ],
    [
      "7009771369859069/1369",
      "-15364593903761431271204353/50653"
    ],
    [
      "30648985263139943/289",
      "4482910575592089590018818/4913"
    ],
    [
      "42964988388252",
      "41074040348284017802"
    ],
    [
      "-1171933235298",
      "346490670641813751746"
    ],
    [
      "241380362084270276/6889",
      "17081211134823369727885090/571787"
    ],
    [
      "39884876978403068/529",
      "-5518539512833845202863266/12167"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,113,550,753,868,1058], T=1889/7. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:19:00",
  "updated_at": "2026-08-27 02:22:31"
}